At the greater emergence of democracy in Europe during the 'Enlightenment' did the papacy support democracy?

One short answer: 1892

The "Ralliement" of the Catholic Church to democracy is often related to the Encyclical "Inter innumeras sollicitudines" (20 Feb 1892) inciting French Catholics to stop trying to restore a King ruling by divine right. France as the biggest Catholic Nation played a great role. However, during the Enlightenment, since the ideas of universal democracy were mainly carried by Libertines, their scriptures were often forbidden.

Two explanations: The meaning of democracy has evolved, and it is only a political system.

"Democracy" was seen (until the eve of the 20th century) as what we call nowadays direct democracy, i.e. the Greek model, with a direct imperative mandate. While considered a very nice model by all (including the church), it was seen as inapplicable to modern nations. How would you gather each week several millions of citizens to make public decisions? How would you use illiterate men elected by their fellow peasants to make a wartime decision?

In Monarchy-ruled France the ultimate national consultative assembly (which also had some power over the Parliaments), the Etats Generaux had not been summoned since 1684 and it took more than a year to gather them in 1788 (the members were elected with an imperative mandate through the "cahiers de doléances" (lists of grievances). A democracy as we know it today seemed very unrealistic, even if it seemed a very good form of government for free cities like the Italian cities).

The famous and very influential Savoyard writer Joseph de Maistre (1753-1821) had previously opposed the stammering democracy of France and the United States as a treacherous form of oligarchy.

The expression of a "General Will" could not be made through votes according to him. Maistre thus attacked the base of the Republic; the French theory of "Représentation Nationale" (no need to translate) which forbid every form of Imperative mandate (the origin of the French rejection of lobbyism). He took the example of the French "Terror" (1793-1795) during which the young Republic obviously failed. He hailed instead the Papal electoral system as the best form of "democracy".

So there was no consensus on "democracy" in Europe until the 20th century (if you consider England a monarchy at that time).

To put it together it is a political question which the church did not really debate (which system is the better? Personally I see no reason to be a fan of democracy -specially if you separate it from the state of law- since it favours corruption and short term politics, but it buys social peace and it enables people to fully enjoy their dignity). But the Church always stressed the equal human dignity at least since the medieval time.

I would separate this from the question of papal control, since the popes had been struggling since ever to maintain control over the Catholic Churchs themselves in Europe (most notably England, France, and the Holy Roman Empire).

For example in France a lot of clergymen rallied the Revolution for their own purposes in this struggle, on all sides (the struggle for the control of the church in France since the 17th century opposed mainly the King backed by some French noble bishops, the Pope and his jesuit supporters as well as noblemen opposed to the King, and the Jansenists reformators backed by some noblemen and bourgeois). Catholics seen as overly favouring the Pope over the French Bishops were called ultramontains (looking over the mountains i.e. over the Alps to Rome) and the ones on the other sides were called gallicans (as in Anglican, Gallica beeing the Latin geographical name for France).